fluffymark | Networking the polymonsterwotsitthingy

This may be a little long. I don't know where I'm going in this post yet, but I'll see where I end up. A few ideas of mine are merging with a few threads from here and there. This has given birth to a new idea to chase, and I've got far too much time on my hands today so I'm going to see how far I get before it doesn't make any more sense. Still with me? Then lets start.

How connected are my friends? Through whom did I meet all of you? I've been pondering this (see, I've got way too much time). Following a recent post of

kmazzy's about how she was introduced to most of her friends, I was inspired to write my own list. First I attempted on the computer, but there were too many names and it got confusing so I attempted to put it all together on paper first. With a pencil. And lots of rubbing out and scribbling and crossing out and reassembling and trying to alter the topology of the paper to get everyone to fit. After several attempts, with some guesswork in some places where I've forgotten, there emerged the following diagram of much doom and scariness:

*boggle* I hope thats not too confusing. The above shows through whom I first got to know most of you - those connected directly to me I met without anyone being strongly involved in how we met or got to know you - otherwise you're linked off the person though whom I first met you or really got to know you. Brackets show those without a LJ who I've added because they are important in linkages. As I suspected,

mirabehn and

doseybat are key to introducing me to many people, but its not that simple, is it? It's far more complicated than that, much more than thought it would be (especially compared to

kmazzy's list). Eeeep. The curious thing is, many of those people, even those far separated on my diagram, are linked to each other. I think I'd need a multidimensional piece of paper to draw all of those, so I've not even tried. But have a look - find yourself and see who else you know on the diagram - see how far away some of them are. The interconnectedness is awesome. And downright scary.

This morning, I'd found that

doseybat had pointed me to a very interesting post about small world syndrome by

rho. All the more curious because I've never met her at all, but the name is familiar, she knows some of my friends, and she describes in highly identifiable terms the meta-group of people I know all too well. Which pretty much shows how insidious this group is already. I've known about this meta-group for many years, but I can't think of a good name for it. The polymonsterthingywotsit with tentacles in everyone. Yes, that one.

This goes far beyond the usual small world connectivity of Milgram's well known "6 Degrees of Separation" back in 1967. I'm told this works because of a few nodes with very high connectiveness that hold the whole thing together. That is the main quality of a Scale Free Network - the Internet itself is a good example, and are many social groups, and there are many others - even Heresy is claimed to be a scale free network. But this monster group doesn't behave like that at all. Looking at my above diagram, I can't point at anyone and say they're the highly connected one that holds the group together. Even if theres a major tragedy and the lovely

mirabehn and

doseybat get abducted by aliens, which would sadden me greatly, I wouldn't actually lose connectivity with the rest. The meta-group is not a scale free network. It's far more connected than that. And it doesn't have to be scale-free. Small-worldedness is not a property limited to scale-free networks. Randomly connected networks exhibit the property well. A very enlightening website here provides a good explanation of the Watts-Strogatz model, showing that short path length can even be obtained even with large clustering. And the meta-group path length is very short - 2 or 3 links at most. This may be a good model for this meta-group - but lets see.

The meta-group is a hybridization of many smaller identifiable sub-groups, each with high connectivity individually. I'm always stunned to find that everyone I know from Oxford seems to know everyone else there (it is true - you do know all each other). Similarly with Cambridge. Then theres the goths, the geeks, the role-players, the bisexuals, etc etc. It just so happens that these groups, for whatever reason, have a high degree of correlation and overlap with each other, and so piling all the groups on top of each other, this enhances the connectivity by many orders of magnitude. The whole thing feeds back on itself and gets even stronger and the tentacles reach out further. Even to those of us on the inside it looks like one big conspiracy. The reason it's so strongly connected has a lot to do with the Internet. Although the Internet itself is scale-free, this doesn't stop communities forming online that aren't scale-free. The usual model of social networks assumes a dynamic construction via preferential attachment - people will seek out the already well-connected popular people, which leads to a few nodes being very highly connected. Somehow this model is flawed here - looking at my diagram above at how my own network dynamically grew, there is no sign of preferential attachment, and every sign that people even not close to me are crucial links. I'd propose that the internet allows one to link to lots of nodes and know lots of people, and not just the highly connected nodes, but except for some rare exceptions, the vast majority of people I know I met them in person first and not online. So that can't be right. But the meta-group is still there. I don't know how big it is, and I suspect it would be impossible to map precisely because it is so interconnected. And it can't be the only one - this phenomena must exist elsewhere? I'm not just talking single large connected groups here (for example Christians, or Jews) - I'm thinking meta-groups where several groups overlap.

Thoughts, ideas? Have I completely lost the plot? Or is it all just a conspiracy just to confuse me? Have I just got too much time to think about silly things like this?